Exponential Function Formula
The exponential function formula gives us the equation of an exponential function where there is a base that is a constant, and an exponent or power which is a variable. In the exponential function formula, the base of the function should be greater than 0. Most often we use the transcendental number e, as the base of an exponential function. Let us understand the exponential function formula in detail along with solved examples in the following section.
What is Exponential Function Formula?
The exponential function grows or decays slowly in the beginning and then changes readily with a small change in time. The rate of change of the exponential function increases with time. The exponential function formula is given as,
f(x) = a^{x}
where,
 a>0 and not equal to 1.
Let us now look at a few solved examples on the exponential function formula to understand the concept better.
Solved Examples Using Exponential Function Formula

Example 1: Simplify the given exponential function by using exponential function formula: 2^{3}.2^{4}
Solution:Given, f(x) = 2^{3}.2^{4}
In the function f(x) = 2^{3}.2^{4}, the bases are the same which is 2
Since the operation is multiplication, we add the powers of the bases.
On adding we get the expression simplified to,
2^{3+4} = 2^{7}Answer: Hence the function 2^{3}.2^{4 }on simplification, becomes 2^{7}.

Example 2: Find the domain of the function by using the exponential function formula:
\[f\left( x \right) = \sqrt {{2^x}  4} \]
Solution: The expression under the squareroot sign must be nonnegative, and so:
\[\begin{array}{l}{2^x}  4 \ge 0\\ \Rightarrow \,\,\,{2^x} \ge 4\,\,\,\Rightarrow \,\,\,{2^x} \ge {2^2}\,\,\, \Rightarrow \,\,\,x \ge 2\\ \Rightarrow \,\,\,D = \left[{2,\infty } \right)\end{array}\]
Answer: The domain of the function is [2,∞).